One of the greatest uses of sleeveless t-shirts is any time when it is very warm. A great example of this is when you are working out at the gym or playing a certain sport. The lack of sleevelees makes it very easy for your arms to breathe so you won't sweat nearly as bad and be much more comfortable. On top of that, these shirts don't allow your sleeves to get caught on anything or get in the way of movement allowing you to be a little bit more flexible.
There are a few different types of this shirt. One of the most common is the 'wife beater' which is also known as an A shirt. The a stands for athletic because that is where they are most commonly used. This may also be called a vest in the UK(they call what we call vests waistcoats). Sleeveless T shirt is also an obvious name for them, because the are simply a T shirt without sleeves.
These shirts can also be made out of many different types of material though the most common is cotton. Cotton is light, breathable, and cheap. There is no need to buy an expensive shirt for most of the things that you will be doing in them. Other materials are not without their advantages however.
One of the things that has caught on recently(relatively, when you consider how long we have worn t shirts) are the stretchy sleeveless t shirts made by companies like under armor(unfortunately you pay a hefty premium for this name). These types of shirt allow you to breathe even more and in some cases literally wick away the sweat from your body. This further helps you stay cool. I have problems with these though. The fact that they are completely skin tight bothers me just because I find it uncomfortable. It is much worse with long sleeve shirts however.
